Yes. The heat it generates is proportional to the voltage being dropped. Using specific examples presented earlier, say the original voltage is 18V and the desired "final" voltage is 15V. So there's a 3V drop in the diodes.
15/18 of the power (83%) goes into the Dispatch Board to light the sign and move the man. 3/18 of the power (17%) is converted to "pure" heat. Of course, in the end, the power into the Dispatch Board becomes heat too as the bulb filaments glow generating heat and the moving figure mechanism warms up from friction and such.
I couldn't find info on the web with actual power numbers (in Watts) for the Dispatch Board. Again, I don't have one of these widgets, but my guess is it might require, say, 10 Watts of power. Skipping some tedious math, this means the diodes would generate about 2 Watts of heat...spread over the 6 diodes (or however many are required). That means each diode is like a 1/3rd Watt heater. I don't know if there's an "official" definition of warm vs. hot, but I'd say the diodes would be warm to the touch but should not burn you finger. My understanding is the Dispatch Board operates intermittently rather than 24/7. In which case I don't think you'd even notice the heat from the circuit.
